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Abstract:

The application relates to a method for determining the cut quality of a
laser cutting process, said quality being assessed on the basis of the
formation of solidification ridges along the cut face and/or burr
formation on the lower edge of the cut face. In said method, a virtual
laser cutting machine in a simulation program can be virtually operated
with a set of values P0 from a parameter space P. In a step a), the
parameter set P0 is entered in the virtual cutting machine (103), then in
step b), a cut is made in the virtual workpiece by calculating, from
partial differential equations with initial and boundary values, the
progression of the melt film thickness over time and the position of the
melt front at the apex of the cutting front according to the depth of the
cut and the time, and then in step c), the spatial distribution of the
ridge amplitude on the cut face is specified by projecting the
progression of the absorption front onto the cut face and/or a spatial
distribution of the burr is calculated from the progression of the melt
film thickness over time and the discharge speed on the lower edge of the
cut face, and in step d), a virtual cut quality is provided (104) for
further analysis.

Claims:

1-15. (canceled)

16. A method for determining the cut quality of a laser cutting process,
said quality being assessed on the basis of the formation of
solidification ridges along the cut face and/or burr formation on the
lower edge of the cut face, whereby in a simulation program a virtual
laser cutting machine is provided that can be operated virtually with a
set of values P0 from a parameter space P, the parameter space P is
defined by
P=(λLaser,l0(t),f(x,z,t),s(x,z,t),p(x,z,t),Pg(x,z,t)-
τg(x,z,t),v0(t),d,Pmaterial), where
Pmaterial=(ρs,cps,λs,ρl,cpl,.-
lamda.l,Hm,Hv,Tm,Tv,η,σ,ncs,ncl, where λLaser represents the wavelength of the laser
radiation, l0(t) the maximum value of the laser radiation intensity
over time, f(x,z,t) the spatial distribution of the laser radiation
intensity over time, s(x,z,t) the spatial distribution of the direction
of the laser radiation over time, p(x,z,t) the spatial distribution of
the polarization state of the laser radiation over time, Pg(x,z,t)
the cutting gas pressure over time, τg(x,z,t) the shear stress
of the cutting gas over time, v0(t) the feed rate, defined as the
relative velocity between the laser beam axis and the workpiece over
time, d the thickness of the sheet metal to be cut, ρs the
density of the material to be cut in the solid state, cps the
specific heat capacity of the material in the solid state, λs
the thermal conductivity of the material in the solid state, ρl
the density of the melt, cpl the specific heat capacity of the melt,
λl the thermal conductivity of the melt, Hm the melting
enthalpy of the material to be cut, Hv the evaporation enthalpy of
the material to be cut, Tm the melting temperature of the material
to be cut, Tv the evaporation temperature of the material to be cut,
η the dynamic viscosity of the melt, σ the surface tension of
the melt, ncs the complex refractive index of the material in the
solid state, ncl the complex refractive index of the melt, and where
x represents the coordinate in the direction of the relative movement
between the material and the laser beam axis and z the coordinate
perpendicular to the top of the material, and t represents the time, said
method comprising the following steps in order to start the virtual
cutting machine: (a) specifying a starting point P0 by acquiring the
machine parameters of a current, real cutting machine, wherein the set of
values P0 is selected from a parameter space P, as defined above,
and the parameter set P0 is entered into the virtual cutting machine
for the sequence of the simulation program, and thereafter starting the
simulation program by (b) making a virtual cut with the virtual cutting
machine that may be based on real values, wherein the progression of the
melt film thickness over time h=h(z,t) and the position M=M(z,t) of the
melt front at the apex of the cutting front is calculated according to
the depth of the cut z (0<z<d, d sheet metal thickness) and the
time t from partial differential equations PDE normalized to v0
∂ h ∂ t + G ( z , t ; h , P 0 )
∂ h ∂ z + D ( z , t ; h , P 0
) = v p , ∂ M ∂ t = v p - 1
##EQU00003## with initial and boundary values h(z,t=0)=h0(z),
M(z,t=0)=M0(z) h(z=0,t)=0, M(z=0,t)=m0(t;P0) where
h0(z) and M0(z) represent any initial distributions,
m0(t;P0) the position of the upper edge of the cutting, front,
vp=vp(z,t) the velocity of the melt front, vs=G(z,t; h,
P0) the flow velocity at the surface of the melt and
D(z,t;h,P0) a damping of the melt film dynamics, for a given
parameter set P0 is calculated from P, and thereafter (c) by a
projection of the time course of the absorption front, defined as the
position M(z,t)-h(z,t), onto the cut face with a transfer function
determined by the feed rate v0 that depicts t on x, specifying the
spatial distribution of the ridge amplitude R(x,z) on the cut face and
calculating a spatial distribution of the burr B(x) at the lower edge of
the cut face from the time course of the melt film thickness h(z=d,t) and
the outflow velocity G(z=d,t; h(z=d,t), P0) at the lower edge of the
cut face, and (d) providing a virtual cutting result comprising at least
one of R(x,z) and B(x), for further assessment, whereby in an additional
step values of the parameters from the parameter space P of the laser
cutting process are determined for the purpose of achieving defined cut
faces and/or for determining the cut faces that can be achieved with a
specified laser cutting machine and/or for configuring components of an
optimized laser cutting machine that meets or at least approximates the
specifications regarding stated requirements on the cut face, by
repeating steps a) to d) each time with changed parameters from the
parameter space P, and wherein rules are derived for the continued and/or
new development of components of a real laser cutting machine from the
values of the parameters from the parameter space P of the laser cutting
process for obtaining defined cut faces that meet or at least approximate
the specifications regarding requirements on the cut faces, if the
determined values cannot be transferred to a real laser cutting machine
with machine-specific parameters, known as machine-specific design space
DM, where DM is the subset of P that can be achieved without
structural changes to the real laser cutting machine.

17. A method as set forth in claim 1, wherein the damping
D(z,t;h,P0) is set to zero in the differential equations DE.

18. A method as set forth in claim 1, wherein in order to calculate the
spatial distribution of the burr B(x) at the lower edge of the cut face,
the Weber number We(t) is determined as the hydro-dynamic characteristic
using h(z=d,t), G(z=d,t; h(z=d,t), P0) and PMaterial.

19. A method as set forth in claim 16, wherein for determining the
parameters at which burr formation through evaporation begins, the
temperature Ts(t)=T(M(z=d,t)-h(z=d,t),z=d,t) is determined on the surface
of the melt, where T(x, z, t) represents the temperature in the melt.

20. A method as set forth in claim 16, wherein one or more characteristic
quantity/quantities K of the ridges and of the burr are derived for the
assessment of the virtual cut quality from the virtual cutting result
consisting of R(x,z) and/or B(x).

21. A method as set forth in claim 16, wherein steps (a) to (d) are
repeated at least once in a vicinity of the parameter set P0 in the
parameter space P, in order to specify for the parameter set P0 the
sensitivities, defined as partial mathematical derivations of the cutting
result or the characteristic quantity/quantities K according to
parameters from P.

22. A method as set forth in claim 16, wherein through mathematical
analysis of the solution structure of the differential equations DE, the
sensitivities, defined as partial mathematical derivations of the cutting
result or the characteristic quantity/quantities K according to
parameters from P are specified for the parameter set P.sub.0.

23. A method as set forth in claim 16, wherein through automatic
differentiating, the sensitivities, defined as partial mathematical
derivations of the cutting result or the characteristic
quantity/quantities K according to parameters from P are specified for
the parameter set P.sub.0.

24. A method as set forth in claim 16, wherein values of the parameters
of the cut that are used to set the spatial distribution of the ridge
amplitude on the cut face are specified, and used to apply an image or a
logo on the cut face.

25. A method as set forth in claim 16, wherein values of the parameters
of the cut are specified for which the physical limits of the smallest
possible ridge amplitude are achieved.

26. A method as set forth in claim 20, wherein solutions of the
differential equations DE are analyzed for their dynamic stability for
different initial values h(z,t=0)=h0(z) and M(z,t=0)=M0(z)
using mathematical methods in order to calculate characteristic
quantity/quantities K, where then, in case unstable solutions exist,
lower limits for the distribution of the ridge amplitude R(x,z) can be
specified based on the degree of instability and thus the respective
characteristic quantity/quantities can be calculated.

27. A method as set forth in claim 16, wherein subsets of P and/or
DM are specified, which meet or at least approximate the
specifications with regard to the requirements regarding the cut faces.

Description:

[0001] The present invention relates to a method for determining the cut
quality of a laser cutting process, which is assessed based on the
formation of solidification ridges along the cut face and/or burr
formation at the bottom edge of the cut face, where in a simulation
program a virtual laser cutting machine is provided that can be operated
virtually using a set of values P0 from a parameter space P.

[0002] Laser cutting is an established separation process. Among the
laser-aided manufacturing methods, it takes the leading position in
industrial applications. From the user's perspective, high productivity
with high quality is demanded for such manufacturing methods.

[0003] Currently, high quality CO2-Lasers (10μ-emitters) with a
radiation wavelength of approx. 10 μm and with a laser power of 1-6 kW
are employed industrially for laser cutting in the field of macro
applications for sheet metal thicknesses ranging from 1 mm to 30 mm. In
addition, new laser sources are available today, such as fiber lasers and
disc lasers (1μ-emitters) with a radiation wavelength of about 1
μm, with a laser power of currently 1-8 kW, and a much better beam
quality than the CO2 lasers. Such 1μ-emitters offer significant
economic advantages over the established 10μ-emitters. However,
1μ-emitters have a poorer cut quality compared to 10μ-emitters,
which is an obstacle to the use of 1μ-emitters.

[0004] The quality of cuts along a workpiece can be assessed based on the
morphology of a ridge structure that forms on the cut face and a burr
formation due to molten material at the lower edge of the cut face. Low
ridge and burr formation are required in addition to flatness and
squareness of the cut face.

[0005] The process chain `cutting-welding` is one example in which the
significance of the quality of the cut face for preparing the joining gap
can be recognized. To be able to generate slim welding seams with a
laser, where said seams require no post-processing by grinding or
dressing, cuts of the components to be joined having plane, right-angled,
smooth cut faces that are burr and oxide free are desired.

[0006] The mechanism that leads to the formation of ridges and burrs as
well as oxide layers along the cut face and the cut edge of the workpiece
was examined for the above reasons. [0007] Ridges arise at the cut face
and the amplitude of the ridges increases abruptly at a certain depth of
the cut, i.e., a change occurs from finer to coarser ridges. [0008] The
amplitude of the coarse ridges becomes greater with an increasing
thickness of the material to be cut. [0009] The coarser ridges are
interrupted repeatedly or exhibit irregular spacing (number of ridges in
the cutting direction changes with the depth of the cut).

[0010] This axial structure or an interruption of the ridges produces an
irregular structure of the cut face and is undesirable. Today, the
achievable ridge amplitude is smaller for the 10μ-emitter than for the
1μ-emitter. [0011] Ridges with the greatest amplitudes caused by the
solidification of molten metal on the cut face occur especially in the
lower part of the cut face or with large material thicknesses. [0012] In
particular with high feed rates the melt does not fully come off the
bottom edge. The attached and then solidifying melt forms the undesired
burr. The mechanisms for the burr formation are understood only to a
certain degree, which means that the potential productivity values of
cutting equipment is significantly under-utilized today. [0013] The
formation of cracks and pores in the weld seam can be caused by oxidized
joining edges, as they occur during flame cutting. For this reason,
fusion cutting is performed with an inert cutting gas to obtain oxide
free cut faces.

[0014] Document EP-B1 0929 376 describes a method for laser beam
treatment, which is said to be particularly suitable for cutting large
material thicknesses of 15 mm or greater. According to this method
several foci are created, which are positioned in the axial direction
along the thickness of the material to produce a large depth effect of
the laser radiation. However, it appears that despite the measures
recommended in this document, the formation of ridges and burrs occurs
with an unchanged severity. Also, the portions of the laser radiation
with a deeper focus lead to an unwanted expansion (rounding) of the kerf
on the upper edge of the material.

[0015] The current state-of-the-art is not sufficient to establish a
quality cut using the 1μ-emitter for a sheet thickness of more than 2
mm and to expand the quality cut to more than 15 mm sheet thickness using
the 10μ-emitter. The reasons for these technical limitations are that
[0016] an extension of the limits for the cut quality cannot be achieved
according to the present experimental experience using 1μ-emitters and
10μ-emitters and with today's available laser and process parameter
settings [0017] the existing understanding about the formation of ridges
and burrs is insufficient to recognize, for example, the necessary,
fundamental new effects of a beam-shaping and then specify beam-shaping
measures.

[0018] For these reasons, experts today only propose measures to improve
the cutting process using 1μ-emitters, which are known from the
experiences of cutting using 10μ-emitters. Thus far, these measures
have been unsuccessful and the 1μ-emitter still cannot achieve the cut
quality of the 10μ-emitter. In addition, no physical cause is known
that could explain the different cut quality.

[0019] The state of the technology and science verifies that at least two
types of ridges exist, namely melting ridges and solidification ridges
with their morphology giving an indication of the underlying formation
mechanism.

[0020] Among others, the document, Schulz W. entitled "Simulation of Laser
Cutting" in The Theory of Laser Materials Processing, edited by J.
Dowden, Springer Series in Materials Science, 2009, Vol. 119, P. 21-69.
ISBN 13 978-1-4020-9339-5, describes the simulation of laser cutting.
Differential equations are listed for this, among other things. The
document also deals with the Weber number. Among others also, the
document, Schulz W. entitled "Dynamics or ripple formation and melt flow
in laser beam cutting", in J. Phys. D: Appl. Phys., 1999, Vol. 32, P.
1219-1228, examines the dynamic behavior of ridge formation and the melt
flow during laser cutting of metals. According to the information given
in these two documents, it is possible to calculate the ridge formation
during laser cutting, i.e., always by specifying interferences that act
on the system from the outside. Only melt ridges are observed according
to these documents.

[0021] Melting ridges form on the upper side of the cut face solely by
movement of the melt front in the absence of solidified melt and have a
small amplitude compared to solidification ridges and are technically of
minor significance.

[0022] Solidification ridges form in greater cutting depth, typically 1 to
2 mm below the top edge of the sheet being cut, by wave-like formation of
the melt front and by wave-like solidifying melt and have a great
amplitude compared to the melting ridges and are technically very
significant.

[0023] According to the state-of-the-art and science, the correlation
between the ridge and burr formation on the one hand and the laser,
machine and material parameters on the other hand is not clarified. For
this reason, making a quality cut using the new laser sources (e.g.,
fiber lasers) is still not mastered, which prevents the wide application
of the new radiation sources and is the subject of worldwide research.

[0024] It is the object of the present invention to provide a method that
allows for the determination of the cut quality of a laser cutting
process by using specific parameters both for a potential real laser
cutting machine that is to be employed and specific parameters of the
material to be cut as well as required process parameters. An options
should also be provided for targeted adjustment of the cut face
roughness.

[0025] This objective is achieved by a method with the features of claim
1. Advantageous embodiments of the method become evident from the
dependent claims. The method according to the invention allows for the
determination of the cut quality of a laser cutting process. According to
this method, the result of the cutting operation to be performed with a
given laser cutting machine, is assessed based on the formation of
solidification ridges along the cut face and/or the burr formation at the
bottom edge of the cut face. This method is not performed on an real
laser cutting machine. Rather, a simulation program provides a virtual
laser cutting machine, which can be operated virtually using a set of
values P0 from a parameter space P. This parameter space P is
defined by

P=(λLaser,l0(t),f(x,z,t),s(x,z,t),p(x,z,t),Pg(x,z,t-
),τ(x,z,t),v0(t),d,PMaterial), where

λLaser represents the wavelength of the laser radiation,
l0(t) the maximum value of the laser radiation intensity over time,
f(x,z,t) the spatial distribution of the laser radiation intensity over
time, s(x,z,t) the spatial distribution of the direction of the laser
radiation over time, p(x,z,t) the spatial distribution of the
polarization state of the laser radiation over time, Pg(x,z,t) the
cutting gas pressure over time, τTg(x,z,t) the shear stress of
the cutting gas over time, v0(t) the feed rate, defined as the
relative velocity between the laser beam axis and the workpiece over
time, d the thickness of the sheet metal to be cut, ρs the
density of the material to be cut in the solid state, cps the
specific heat capacity of the material in the solid state, λs
the thermal conductivity of the material in the solid state, ρl
the density of the melt, cpl the specific heat capacity of the melt,
λl the thermal conductivity of the melt, Hm the melting
enthalpy of the material to be cut, Hv the evaporation enthalpy of
the material to be cut, Tm the melting temperature of the material
to be cut, Tv the evaporation temperature of the material to be cut,
η the dynamic viscosity of the melt, σ the surface tension of
the melt, ncs the complex refractive index of the material in the
solid state, ncl the complex refractive index of the melt, and where
x represents the coordinate in the direction of the relative movement
between the material and the laser beam axis, and z the coordinate
perpendicular to the top of the material, and t represents the time.

[0026] According to the method, the parameter set P0 is entered into
the virtual cutting machine for the simulation program sequence in a step
(a).

[0027] Then in a step (b), a virtual workpiece is created in a virtual
cutting operation using the virtual cutting machine by developing the
melt film thickness h=h(z,t) and the position M=M(z,t) of the melt front
at the apex of the cut front over time as a function of the cut depth z
(0<z<d, d sheet metal thickness) and the time t from the partial
differential equations PDE normalized to v0

[0029] where h0(z) and M0(z) represent any initial
distributions, m0(t;P0) the position of the upper edge of the
cutting front, vp=vp(z,t) the velocity of the melt front,
vs=G(z,t; h, P0) the flow velocity at the surface of the melt
and D(z,t;h,P0) a damping of the melt film dynamics,

and for a given parameter set P0 is calculated from P.

[0030] Then, in a step (c) by a projection of the time course of the
absorption front, defined as the position M(z,t)-h(z,t), onto the cut
face with a transfer function determined by the feed rate v0 that
depicts t on x, the spatial distribution of the ridge amplitude R(x,z) on
the cut face is specified. Additionally or alternatively, a spatial
distribution of the burr B(x) at the lower edge of the cut face is
calculated from the time course of the melt film thickness h(z=d,t) and
the outflow velocity G(z=d,t; h(z=d,t), P0) at the lower edge of the
cut face.

[0031] Finally, in step (d) a virtual cutting result comprising R(x,z)
and/or B(x), is provided for further assessment.

[0032] Thus, the method according to the invention utilizes a virtual
cutting machine to calculate the formation of solidification ridges at a
virtual cut face and the burr formation at the bottom of the virtual cut
face with the use of the differential equations DE. In particular the
method can be used to specify a time-related modulation of the cutting
parameters, which in turn can be used to set the spatial distribution of
the ridge amplitude on the cut face. The differential equation
∂M/∂t=vp-1 is a non-dimensional equation; the
parameters are scaled to the reference parameter, the feed velocity
v0, wherein the feed velocity v0 is defined as the relative
speed between laser beam axis and workpiece. The differential equation
for vp is also scaled to v0.

[0033] This ability to set the ridge amplitude on the cut face in a
defined manner can be used not only to keep the ridges as small as
possible, but also to represent an image or a logo on the cut face. One
area of application of the method according to the invention, however, is
to specify those cutting parameters for which the physical limit of the
smallest possible ridge amplitude is reached. The words "the smallest
possible ridge amplitude" here means that under certain cutting
conditions ridges will remain despite an optimization of the cutting
conditions, where such ridges occur through technically unavoidable
fluctuations of the cutting parameters and therefore cannot be eliminated
but only limited to smaller values.

[0034] The simulation program, which is the basis of the method according
to the invention, uses the knowledge that solidification ridges and burrs
form by excitation of axially traveling waves at the apex of the cutting
front, which means removal fluctuations arise at the apex of the cutting
front, and that there are two physical reasons for this.

[0035] It is known that ridges and burr occur [0036] due to instability
inherent in the cutting process and with specified stability limits, and
[0037] due to external interferences, which [0038] can be caused by
unavoidable fluctuations of laser and machine parameters, or [0039] by
spatial fluctuations in the material properties (e.g., grain boundaries),
or [0040] can be due to an intentionally set modulation of the
parameters of the cutting process (e.g., modulation of the laser
radiation or of the cutting gas flow).

[0041] The simulation program is based on a physical ridge model with
which the spatial distribution of the ridge amplitude R can be calculated
on the cut face. The ridge amplitude R=R(x,z) depends on the cutting
position x along the cut face and the cutting depth z, as well as cutting
parameters P.

[0042] The set of values of P0 from the parameter space P consists of
laser, machine and material parameters and, among other things takes into
account spatially distributed parameters such as the intensity of the
laser radiation and the driving forces--these are the spatial gradient of
the gas pressure and the shear stress of the gas at the surface of the
melt film--of the cutting the gas flow on the melt to be driven out.

[0043] It is also essential that in addition to the mean values of the
parameters this set of parameters also contains their technically
unavoidable fluctuations.

[0044] Furthermore, this set of parameters also contains in addition to
the mean values of the parameters and their technically unavoidable
fluctuations intentionally set temporal modulations. The productivity,
for example the cutting speed, can be increased by a temporal modulation
of the parameters, and this optimization can be carried out by the
simulation program on a virtual laser cutting machine and therefore at
low cost. This optimization opportunity is provided in that the ridge
morphology can be adjusted in a targeted manner by a temporal modulation
of the parameters, such that defined structures can be generated for the
ridges to a minimization of the ridge structure. When cutting, this
modulation may be used ultimately to also form a logo or an image on the
cut face.

[0045] The burr formation at the cut face is also taken into account in
the simulation program by computing and considering the properties of the
resulting burr through utilizing the physical ridge model and from the
calculated ridge amplitude R(x,z). A burr can be characterized by the
following parameters [0046] The burr width bB in the feed
direction and hence the distance measured in the feed direction, where
the solidified melt adheres to the underside of the sheet metal or the
bottom edge of the cut face, [0047] The burr volume VB; the volume
of solidified melt that adheres to the underside of the cut sheet metal,
i.e., below the lower cut edge, [0048] The burr height hB; this is
the height of the solidified melt that adheres to the underside of the
cut sheet metal.

[0049] Thus, the simulation program also takes into account whether the
burr consists of a kind of burr beads, or a kind of burr strings. By
definition, a burr bead forms where the burr height hB is less than
or equal to the burr width bB, while a burr string arises when the
burr height hB is greater than the burr width bB.

[0050] In the set of values P0 of the parameter space P,
thermo-physical parameters, such as the melting temperature Tm and
the vaporization temperature Tv of the melt film surface at the
lower edge, and material parameters, such as the surface tension of the
melt, are taken into account as well.

[0051] The method according to the invention is used for laser cutting
with reactive cutting gas beam and for laser cutting with inert cutting
gas beam. With respect to the latter method, distinctions are made
between the variants beam fusion cutting, quick cutting and high-speed
cutting.

[0052] Based on the simulation program and by specifying a virtual laser
cutting machine that meets the ideal conditions and is universally
adjustable, the theoretically optimal values Popt can be determined for
the parameters P for one predefined ridge morphology (e.g., minimal
roughness) and a burr-free cut face by varying the parameter values
P0 through repeating the steps a) to d) each time with different
parameters from the parameter space P.

[0053] The cutting machines available today are not technically perfect
and exhibit a restricted design space depending on the manufacturer. The
theoretically optimal sets of parameters from the virtual cutting machine
resulting from the method according to the invention by applying the
simulation program cannot always be implemented in a real cutting
machine. Therefore, the results obtained with the simulation program are
used to Improve a real laser cutting machine in certain parameters or
even to dimension it anew, by determining based on the results of the
simulation program the causes or the parameters that lead to an
undesirable development of the ridge amplitude and/or to unwanted burr
formation. For this purpose, the individual values P0 of the
parameter space P are viewed and analyzed in order to then select and
change those values from the parameter space P that lead to the best
approximation of the values P0 of the parameter space P.

[0054] Such an approximation is thus based on a virtual path and can also
be accomplished by iterative changes in the values P0 of the
parameter space P. If necessary, the found, approximate parameters can be
verified in real cutting experiments. From the information obtained via
the method, required process parameters or boundary conditions for the
required components of the laser cutting machine can be derived that
concern the shaping of laser radiation and the cutting gas flow.

[0055] An essential step in the method according to the invention lies in
the mathematical-physical calculation of ridges on the cut face and the
burr formation. This calculation is based on a high-dimensional set of
coupled, nonlinear, partial integro-differential equations (differential
equations, which, in addition to derivatives also contain the integrals
of the dynamic variables) of at least the fifth order, with some of the
involved partial differential equations are of the known
Kuramoto-Sivashinsky type. However, in order to solve this complex task,
the method according to the invention is based on a greatly simplified
system developed by the inventor, said system comprising only two partial
differential equations of the first order for only two variables in order
to replace the differential equations of the higher orders.

[0057] where h0(z) and M0(z) represent any initial
distributions, m0(t;P0) represents the position of the upper
edge of the cutting front, vp=vp(z,t) represents the speed of the melt
front, vs=G(z,t; h, P0) represents the flow velocity at the
surface of the melt and D(z,t;h,P0) represents a damping of the melt
film dynamic, a temporal development of the melt film thickness h=h(z,t)
and of the position M=M(z,t) of the melt front at the apex of the cutting
front is calculated as a function of the cutting depth z (0<z<d, d
sheet metal thickness) and the time t.

[0058] For the remaining quantities that can enter into the model that
underlies the simulation program and that are to be specified at the apex
of the cutting front, different physical models known from the literature
can be used to determine the parameters [0059] Position
m0(t;P0) at the upper edge of the cutting front [0060] Velocity
vp=vp(z,t) of the melt front [0061] Flow velocity
vs=G(z,t; h, P0) at the surface of the melt [0062] Damping D
(z,t; h, P0) of the melt film dynamic.

[0063] Different levels of approximation can be specified for the
calculation of these quantities.

[0064] It shall be taken into account that the velocity of the melt front
vp=N[M-h, QA] couples the two differential equations in a
nonlinear manner. The velocity vp of the melt front is calculated by
a nonlinear operator N, which depends also on the absorbed energy flux
density QA.

[0065] The absorbed energy flux density QA,

QA=μA(μ)I0f(x,z;t)|x=M-h, μ=cos(sn),

[0066] is calculated from the cosine of the angle of incidence μ, the
absorption coefficient A(μ) of the maximum intensity l0 and the
distribution f (0<f<l) of the laser radiation intensity. The angle
of incidence is enclosed by the direction vector s of the energy flux
density of the laser and the normal vector n of the surface of the melt
film. The distribution f (0<f<1) of the intensity depends on the
spatial coordinates x, z, with x representing the feed velocity and z the
direction of propagation of the radiation, and of parameters Pf that
are used to parameterize the distribution.

[0067] The flow rate vs=G(z,t; h, P0) at the surface x=M-h of
the melt is specified by a function G, which is determined from the flow
of the cutting gas and the flow of the melt.

[0068] The damping D(z,t;h,P0) in the differential equations DE can
be set to zero in certain models and is thus not considered.

[0069] The properties of the resulting burr are calculated utilizing the
physical ridge model and from the ridge amplitude R(x,z=d) at the lower
edge of the cut face calculated from it according to the invention as
follows:

[0070] The burr width bB in the feed direction--that is the distance
measured in the feed direction on the underside of the sheet metal, where
the solidified melt adheres--is calculated by
bB=v0(t2-t1), where v0 is the feed speed.
According to the invention, the out flowing melt cannot separate between
the times t1 and t2, and thus adheres to the sheet metal and
solidifies. The time t1 is determined by the condition

We=We(h(z=d,t);P0)<Wecrit,

[0071] where the quantity We

We=(pvs2)/(σ/hd)

[0072] is referred to as the Weber number with hd specifying the
dimensional thickness of the melt film on the underside of the sheet
metal. The time t2 is defined by the condition We>Wecrit,
thus, the time span t2-t1 is the time interval during which We
drops below Wecrit. For the quantities vs=G(z,t; h, P0)
and hd, the solution from the physical ridge model shall be entered
in the expression for the Weber number. The value Wecrit shall be
determined separately and physical models or experimental results can be
used for this.

[0073] The Weber number We is a dimensionless characteristic, which serves
as a measure for a bead deformation. The larger it is, the greater is the
deformation effect and the farther away the bead has moved from the
spherical shape. The relationship between the burr formation and the
Weber number is known in the art.

[0074] The referenced burr volume VB, i.e., the volume of the
solidified melt that adheres underneath the cut sheet metal is determined
using the found value for the burr width bB=v0
(t2-t1). With this value for the burr width bB=v0
(t2-t1), the outflow velocity vs and the condition
VB=V (t2-t1), wherein the volume V(t2-t1) is
determined by the melt that flows out at the bottom z=d in the interval
t2-t1, the value for the burr volume VB follows.

[0075] The burr height hB, i.e., the height of the solidified melt
that adheres below the cut sheet, is calculated from the solution
h(z=d,t) of the differential equations DE and the values for the burr
width bB and the burr volume VB.

[0076] By a projection of the time course of VB(t) with a transfer
function that is determined by the feed speed v0 and that displays t
on x, the spatial distribution of the burr volume/burr height can be
specified along the lower edge of the cut face hB(x).

[0077] Further, for determining the parameters at which burr formation
through evaporation begins, the temperature
Ts(t)=T(M(z=d,t)-h(z=d,t),z=d,t) can be determined on the surface of
the melt, where T(x,z,t) represents the temperature in the melt. The
temperature in the melt is determined by applying the heat conduction
equation. When Ts is >vaporization temperature Tv, then a
burr formation occurs.

[0078] To assess the virtual cut quality, one or more characteristic(s) K
of the ridges, such as the roughness of the cut face Rz and of the
burr, e.g., the burr volume VB, the burr height hB, the burr
width bB are derived from the virtual cutting result, consisting of
R(x,z) and/or B(x). The choice of which characteristic is used is up to
the respective user of the method. The characteristic quantities are
selected user-specific, and R(x,z) and/or B(x) are sufficient for the
assessment of the cut quality.

[0079] In order to optimize the respective quality of a method procedure
even further, steps a) to d) of the method, as indicated in claim 1, are
repeated at least once in a vicinity of the parameter set P0 in the
parameter space P. This allows for specifying the sensitivities, defined
as partial mathematical derivatives of the cutting result or
characteristic(s) K according to parameters of P for the parameter set
P0.

[0080] Through an alternative process measure, namely by mathematical
analysis of the solution structure of the differential equations DE,
these sensitivities, defined as partial mathematical derivatives of the
cutting result or of the characteristic(s) K according to parameters of
P, of the parameter can be specified.

[0081] Another alternative method for specifying the sensitivities is the
one by automatic differentiation. Automatic differentiation is a
mathematical method known in the art, to form partial mathematical
derivatives of a function.

[0082] By repeating the method steps (a) to (d) of the method according to
claim 1, each time with changed parameters from the parameter space P,
values of the parameters from the parameter space P of the laser cutting
process are determined for the purpose of obtaining defined cut faces
and/or for determining the cut faces that can be achieved with a
specified laser cutting machine, and/or for configuring components of an
optimized laser cutting machine that meets or at least approximates the
specifications regarding requirements for the cut faces.

[0083] From the foregoing process measure rules can be derived for the
continued and/or new development of components of a real laser cutting
machine via the values of the parameters from the parameter space P of
the laser cutting process for obtaining defined cut faces that meet or at
least approximate the specifications regarding requirements on the cut
faces, if the determined values cannot be transferred to a real laser
cutting machine with machine-specific parameters, known as
machine-specific design space DM, where DM is the subset of P
that can be achieved without structural changes to the real laser cutting
machine.

[0084] In order to apply an image or a logo on the cut face, values of the
cutting parameters, potentially spatially and time-dependent values, are
specified with which the spatial distribution of the ridge amplitude is
to be set on the cut face.

[0085] For a special case, in which the specification calls for the lowest
possible ridge amplitude, cutting parameters are specified, for which the
physical limit of the smallest possible ridge amplitude is achieved,
which may be limited, for example, by technically unavoidable
fluctuations of the cutting parameters.

[0086] To calculate the characteristic(s) K, which are used to assess the
cut quality in accordance with the stated requirements, an advantageous
embodiment of the method according to claim 1 is to analyze different
solutions of the differential equations DE using mathematical methods for
their dynamic stability for different initial values h(z,t=0)=h0(z)
and M(z,t=0)=M0(z). If unstable solutions exist, lower limits for
the distribution of the ridge amplitude R(x,z) can be specified from the
degree of instability, and the respective characteristic(s) K calculated.

[0087] Also, subsets of P or DM can be specified, which meet or at
least approximate the specifications with regard to the requirements
regarding the cut faces. Such subsets of P (parameter space) and DM
(design space) are limits that the user would like to adhere to in
designing his laser cutting system and/or the cutting process.

[0088] The basic procedure of the method according to the invention is
based on the schematic diagram briefly explained below and shown in the
accompanying FIG. 1.

[0089] The method according to the invention, as shown in the diagram,
employs a virtual cutting machine, which is designated with the reference
character 100. For the implementation of the method, for one the design
space DM is acquired, step 101, and secondly, the required cut quality
entered, step 102. A cost function to be minimized can be specified in
step 102 as well.

[0090] To start the virtual cutting machine 100, a start point P0 is
specified in step 103, for example by detecting the machine parameters of
a current, real cutting machine. The set of values of P0 is selected
from the parameter space P, as is defined in greater detail above.

[0091] The simulation program is started by creating a virtual cut with
the virtual cutting machine, which can be based on real values. The
simulation program outputs a result of the cutting that includes the
spatial distribution of the ridge amplitude R(x,z) on the cut face and
the spatial distribution of the burr B(x) at the lower edge of the cut
face.

[0092] The quality of cutting is assessed in step 104.

[0093] In step 105 a decision is made whether the virtually determined cut
quality conforms to the specification of the required cut quality (step
102). If this is the case, the sequence of the process proceeds to step
106, where an examination is made if the set of values P0 from the
parameter space P is consistent with the design space DM of the
machine, which was input in step 101.

[0094] If it is decided in step 105 that the cut quality does not
correspond to the required cut quality, the sequence proceeds to step
107, where the set of values P0 of the parameter space P are
altered. Such a variation may for example be based on the sensitivities
that are obtained through one of the methods according to claims 6 to 8.
The altered values P0 are then used to operate the virtual cutting
machine 100.

[0095] The loop across the process steps 105, 107 and 104 is repeated
until in step 105 the cut quality corresponds to the required cutting
results.

[0096] If the query in step 106 is negated, the process ends in step 108;
in step 108, the statement is made that a structural change of features
of the real laser cutting machine, whose parameters (design space DM)
have been used to run the simulation program, is required to meet or at
least to approximate the specifications stated in step 102 of the
required cut quality.

[0097] If the response to the query in step 106 is affirmative, the method
proceeds to step 109; in step 109, a new set of values P0 from the
parameter space P is applied to the real laser cutting machine with
parameters that have been specified in step 103 or in step 107.

[0098] In step 110, a cut made with the real laser cutting machine is then
tested.

[0099] A real cutting machine can thus be configured by determining which
values of the cutting parameters P lead to an undesired development of
the ridge amplitude and/or lead to unwanted burr formation and what
presents the best approximation Pan of the parameters P to the
desired cut quality, which are the theoretically optimal values
Popt.

[0100] To do this, the design space of the real cutting machine is
determined. The design space of the real cutting machine contains the
real adjustable values Preal of the parameters from P. By applying
the virtual laser cutting machine, the values Pan of the parameters
are found, which achieve the best approximation to the desired cut
quality.

[0101] The quality is tested on the real cutting machine. A potentially
remaining discrepancy between the desired and achieved cut quality on the
real cutting machine can be improved by iterative refinement of the
determination of the design space. The invention can always be employed
when during laser cutting the predominant portion of the melt is removed
in front of or adjacent to the laser beam.

Patent applications by Markus Niessen, Niederzier DE

Patent applications by Wolfgang Schulz, Langerwehe DE

Patent applications in class MODELING BY MATHEMATICAL EXPRESSION

Patent applications in all subclasses MODELING BY MATHEMATICAL EXPRESSION